We first present a nonlocal isoperimetric problem for three interacting phase domains, related to the Nakazawa-Ohta ternary inhibitory system which describes domain morphologies in a triblock copolymer. We consider global minimizers on the two-dimensional torus, in the droplet regime where some of the species have vanishingly small mass but the interaction strength is correspondingly large. In this limit there is splitting of the masses, and each vanishing component rescales to a minimizer of an isoperimetric problem for clusters in 2D. These results have led to a new type of partitioning problem that I will also describe. These represent work with S. Alama, X. Lu, C. Wang, S. Vriend and M. Novack.
